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Let X={xi:1≤i≤n}⊂N+, and h∈N+. The h-iterated sumset of X, denoted hX, is the set {x1+x2+…+xh:x1,x2,…,xh∈X}, and the [h]-sumset of X, denoted [h]X, is the set ⋃i=1hiX. A [h]-sumset cover of S⊂N+ is a set X⊂N+ such that S⊆[h]X. In this paper, we focus on the case h=2, and study the APX-hard problem of computing a minimum cardinality [2]-sumset cover X of S (i.e. computing a minimum cardinality set...
Given an undirected graph G with n nodes and m edges, we address the problem of finding a largest collection of edge-disjoint cycles in G. The problem, dubbed Cycle Packing, is very closely related to a few genome rearrangement problems in computational biology. In this paper, we study the complexity and approximability of Cycle Packing, about which very little is known although the problem is natural...
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